Related papers: Primely generated refinement monoids
We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We…
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the…
This is an essay about a certain family of elements in the general linear group GL(d,q) called primitive prime divisor elements, or ppd-elements. A classification of the subgroups of GL(d,q) which contain such elements is discussed, and the…
The celebrated minimum residual method (MINRES), proposed in the seminal paper of Paige and Saunders, has seen great success and widespread use in solving Hermitian (and complex-symmetric) linear systems. Unless the system is consistent,…
In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a…
We prove the a priori bounds for infinitely renormalizable quadratic polynomials for which we can find an infinite sequence of primitive renormalizations such that the ratios of the periods of successive renormalizations is bounded. This…
In the present paper, we define the generalized Kwang-Wu Chen matrix. Basic properties of this generalization, such as explicit formulas and generating functions are presented. Moreover, we focus on a new class of generalized Fubini…
We give a classification of noncommutative algebraic monoid structures on normal affine varieties such that the group of invertible elements of the monoid is connected, solvable, and has a one-dimensional unipotent radical. We describe the…
We develop a complex differential geometric approach to the theory of higher residues and primitive forms from the viewpoint of Kodaira-Spencer gauge theory, unifying the semi-infinite period maps for Calabi-Yau models and Landau-Ginzburg…
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…
Transformation formulas for four-parameter refinements of the q-trinomial coefficients are proven. The iterative nature of these transformations allows for the easy derivation of several infinite series of q-trinomial identities, and can be…
This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…
We answer a question of Margolis from 1997 by establishing that the maximal subgroup of the minimal ideal of a finitely generated free profinite monoid is a free profinite group. More generally if $\mathbf H$ is variety of finite groups…
We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…
We generalize the Poisson-Lie T-duality by making use of the structure of the affine Poisson group which is the concept introduced some time ago in Poisson geometry as a generalization of the Poisson-Lie group. We also introduce a new…
Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.
We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known…
In our recent paper [Sh1] a version of the "generalized Deligne conjecture" for abelian $n$-fold monoidal categories is proven. For $n=1$ this result says that, given an abelian monoidal $k$-linear category $\mathscr{A}$ with unit $e$, $k$…
Answering a question of Dan Haran and generalizing some results of Aschbacher-Guralnick and Suzuki, we prove that given a set of primes pi, any finite group can be generated by a pi-subgroup and a pi'-subgroup. This gives a free product…
The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…